The basic unit of information processing in modern day computers is a bit, which can exist in one of two states: 0 or 1. In quantum computing the basic unit of information processing is a qubit. Like a bit, the qubit can also exist in two states, which states are denoted as state |0 and state |1. But unlike a bit, a qubit can also exist in superposition states, which are a linear combination of state |0 and state |1. For example, if the qubit were to be denoted by |ψ, then the superposition states of the qubit can be described by the expression: |ψ=α|0+β|1, where α and β are complex amplitudes (also known as probability amplitudes). Therefore, the qubit |ψ can exist in any of the states described by the continuous variables α and β. This property of qubits is essential in quantum computing. Therefore, if the qubit |ψ is prepared in a superposition state for quantum computing, then it is essential that the superposition state of the qubit |ψ be maintained throughout the computing process.
Results of a quantum computation require that one or more qubits of the quantum computer be measured. Two kinds of measurements can be carried out on the qubit |ψ: a strong measurement and a weak measurement. In a strong measurement, the qubit ceases to exist in the superposition state, and collapses into one of its so-called eigenstates. For the qubit |ψ, these eigenstates are the states |0 and |1. Therefore, after a strong measurement, the qubit |ψ will collapse in a state |0 or state |1 . An example of a strong measurement is a detector detecting a click in a cavity quantum electrodynamics (QED) system implementing the qubit |ψ, where measuring a click indicates that the qubit |ψ has collapsed into state |1. Because of the collapse of the superposition state, information related to the original state of the system cannot be recovered. In other words, the values of α and β (also known as the eigenvalues) are lost.
In a weak measurement, the full collapse into the eigenstate does not take place, and it is possible, to reverse the measurement so that the original state of the system is restored. This reversal is possible, because for weak measurement, the full information of the probability amplitudes involved in the superposition of the states is retained. One example, of a weak measurement is the leakage of the field inside a cavity QED system. If a measurement is made on the qubit |ψ using a detector, and the detector registers a click, then this means that qubit |ψ has collapsed to the state |1. Thus, the information on amplitudes α and β is lost and no longer recoverable. This, of course, indicates a strong measurement. If however, the detector does not register a click for time τ, then the state evolves into |ψ(τ)=(α|0+e−γτβ|1)/√{square root over (|α|2+|β|2e−2γτ)} where γ is the cavity decay rate. This is an example of a weak measurement where we gain partial information on the state of the qubit |ψ, but information of the amplitudes α and β is fully retained. Note that the above equation can also describe a weak measurement on a qubit implemented in systems other than the cavity QED system with γ representing the decay rate of the qubit for a particular system. Thus, unlike strong measurements, weak measurements provide the possibility of restoring the qubit to its original superposition state.
Some prior art methods propose reversing the state of the qubit |ψ after a weak measurement by carrying out a second weak measurement. For example, the states |0 and |1
are first switched to transform the weak state α|0+e−γτβ|1 to α|1+e−γτβ|0. A second weak measurement (e.g., a cavity decay without registering a click in the detector) for time τ then yields α|1+β|0. A subsequent interchange between |0 and |1 restores the original state of |ψ=α|0+β|1. For additional details of this method, the reader is referred to Exhibit C of the '959 application.
While the prior art method including two weak measurements to restore the original state of the system is adequate, the inventors recognize that the time required for the second weak measurement is disadvantageous. One of the biggest challenges in quantum computing is decoherence. Decoherence can be viewed as the irrecoverable loss of information from a quantum computer due to the interactions with the environment. Once the quantum computer has decohered, the computations are no longer useful. Each quantum computer, depending upon the quantum system used to implement it, has an associated decoherence time. Therefore, it is important to complete quantum computations within decoherence time.
A quantum computer involves computations that typically include a large number of qubits interacting with each other. Therefore, time spent for restoring a qubit would increase the computation time of a computation in which the qubit is involved. In the case of a weak measurement, waiting for another period τ to restore the qubit can increase the total computation time of the quantum computer, which computation time if comparable to the decoherence time can make the quantum computer unreliable.
A solution to these problems is provided in this disclosure in the form of a new reversal quantum gate circuit, which does not require a second weak measurement and reduces the time required for reversal when compared to the two weak measurement method.